Sunday, March 11, 2007

My First Financial Mistake

... or is it?? I am not yet sure, given that I don't know the rate of interest that would have been charged to me by my bank.

A couple of days back I made an online transaction to the tune of just under Rs. 35000/- The actual value had to be paid in dollars. So the most legitimate way is to pay through your credit card, which in essence would reflect on your finance statement. The other not so legal way would have been to ask a friend in the concerned country to pay for me while I remit the equal value in Indian Rupees to him through some other channel locally, probably his relatives, in India. I chose the first.

Now comes the part where I need to repay my credit card. Although my company pays me well (ok, good!), some investments and some lifestyle spends leaves me with little cash at the end of the month. Basically, I live from one month to the next month's salary. Which leads me to the situation where Rs. 35000 is a big sum to be paid in one installment, and I need a loan to repay the amount.

Besides a lot of other "attractive" facilities, my credit card allows me to convert my expenditure into Equated Monthly Installment (EMI). So if I have made a single purchase of value more than Rs. 1500 and need an extension of credit, my credit agency would gladly convert that into an EMI of 6, 12 or 24 months by charging me at the rate of 12%, a processing fee and applicable taxes. Obviously I need to call up and ask for it. Otherwise the nominal annual percentage rate (APR) is 2.95% per month (35.4% per annum), which converts to an effective annual rate (EAR) of 41.74%, which is a bit on the higher side. For the sake of convenience I opted for a 6 month payment option.

There was the other option of calling up my bank which, last heard, would have offered me a loan for the same amount at an annual rate of 11%. Here in comes the convenience part. My bank, although I have to maintain my salary account with them, requires certain documents before they advance me the amount. The actual documents required is very nominal: residence proof in some specific template, payslips, etc. etc. It would have taken me approximately a week to arrange for it all. Compared to this my credit card company does not require any extra documents since my credit worthiness is already established with them.

Now the question is how much did I pay for this convenience. For this I needed the interest rates offered to me by my bank and my credit card company. And when I actually sat down to calculate the interest that I would pay, I found I could not recall a single thing about how to go about it. Wow!!! After 25 years of formal education, I did not know how to calculate interest on a loan. And I had to sit down with pen and paper.

Take it easy. Begin with a few assumptions for both cases: (i) interest would be compounded monthly (ii) processing fee charged would be approximately same (iii) the rate of interest by the bank is 11% and the credit card company is 12% (iv) while the credit card company would extend me a 6 month loan, my bank would do it for a minimum of 12 months.

In itself calculating the amount of interest to be paid is easy, but it required some thought. First realization: one side of the equation is the monthly compounded value of the loan amount, L, after n months at an interest rate of r% p.a. (= L*[1+r/12]^n), where r is divided by 12 (to convert into monthly interest rate) and 100 (to convert into decimals from percentage form).

The other side of the equation would be value of repayments in form of EMI, E, that I would make on a monthly basis, again compounded monthly (= E*[1+r/12]^[n-1] + E*[1+r/12]^[n-2] + ... + 1 ).

Equating these two would give the value of E (EMI) to be

E = L * r * ( [1+r/12]^n ) / ( [1+r/12]^n -1 ).While this is one way of calculating, another method is shown here. Albeit I find it a bit more round about and a bit more complex. Anyways, putting actual values into the equation reveals the following scenario.

If I take the credit card company option, I would be repaying the loan by paying an approximate EMI of Rs. 6100 (approx) for 6 months. While if I take my bank's loan option for 12 months, I will be paying an EMI of Rs. 3100 (approx). While the second option seems costlier by Rs. 600, actual calculation would not vary much from it.

But, but, but... is it the most viable option?? Here we need to consider the time value of money. Which would a full topic by itself. A simple explanation would be if I can take that Rs. 3000 extra per month from the 6 months and keep investing it and then it out after 6 months and use it to pay the rest of the installments for the 12 month option, I would be left over with something extra. But how much is the question. Will it just be enough to pay for the difference in both terms or will I have more??